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1/5+1/14+1/28+1/44+1/61+1/85+1/97 =0,3683
1/2 = 0,5
0,3683<0,5 nên 1/5+1/14+1/28+1/44+1/61+1/85+1/97 < 1/2
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Ta có \(\frac{1}{5}=\frac{1}{5}\)
\(\frac{1}{14}< \frac{1}{10};\frac{1}{28}< \frac{1}{10}\)
\(\frac{1}{44}< \frac{1}{40};\frac{1}{61}< \frac{1}{40};\frac{1}{85}< \frac{1}{40};\frac{1}{97}< \frac{1}{40}\)
\(\Rightarrow\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{44}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}< \frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{40}+\frac{1}{40}+\frac{1}{40}+\frac{1}{40}=\frac{1}{5}+\frac{1}{5}+\frac{1}{10}=\frac{5}{10}=\frac{1}{2}\)\(\Rightarrow A< \frac{1}{2}\)
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Sai đề. Sửa đề :v
Cmr: \(\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}< \dfrac{1}{2}\)
Giải:
Đặt \(A=\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}\)
Ta có:
\(A=\dfrac{1}{5}+\left(\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}\right)+\left(\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}\right)\)
\(A< \dfrac{1}{5}\left(\dfrac{1}{14.3}\right)+\left(\dfrac{1}{61.3}\right)\)
\(A< \dfrac{1}{5}+\dfrac{3}{14}+\dfrac{3}{61}\)
\(A< \dfrac{1}{5}+\dfrac{3}{12}+\dfrac{1}{20}\)
\(A< \dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}\)
\(\Rightarrow A< \dfrac{1}{2}\)
Vậy \(\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}< \dfrac{1}{2}\) \((đpcm)\)
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Đặt A=15+114+128+144+161+185+197
Ta có:
A=15+(114+128+144)+(161+185+197)
A<15(114.3)+(161.3)
A<15+314+361
A<15+312+120
A<15+14+120
⇒A<12
Vậy 15+